(a) Given that (sin alpha = 0.3907), use tables to find the value of : (i) (tan alpha) ; (ii) (cos alpha).
(b) A ladder of length 4.5m leans against a vertical wall making an angle of 50° with the horizontal ground. If the bottom of a window is 4m above the ground, what is the distance between the top of the ladder and the bottom of the window? (Answer correct to the nearest cm)
Explanation
(a) Given (sin alpha = 0.3907)
From the sine table, (alpha = 23°)
(i) (tan alpha = tan 23° = 0.4245)
(ii) (cos alpha = cos 23° = 0.9205)
(b) Let T be the top of the ladder and B, the bottom of the vertical wall.
From the figure, (sin 50° = frac{BT}{4.5m})
(BT = 4.5 sin 50° = 4.5 times 0.7660)
(BT = 3.447m)
Distance between the top of the ladder and bottom of the window
= (4 – 3.447 = 0.553m)
= ( 0.553m times 100)
= (55.3 cm)